Figure (a) shows a narrow charged solid cylinder that is coaxial with a larger charged cylindrical shell. Both are nonconducting and thin and have uniform surface charge densities on their outer surfaces. Figure (b) gives the radial component E of the electric field versus radial distancer from the common axis. The vertical axis scale is set byEs = 4.8 × 103 N/C. What is the linear charge density of the shell?
A cylinder of radius just under r cm encloses only the solid cylinder and has an electric field of Es/3 at its surface.
Apply Gauss’s law:
2π(rcm)L(Es/3) = λL/e, where L is the length of the Gaussian cylindrical surface.
The L’s on both sides cancel, and one can solve for the charge per unit length, λ.
We get:
2π(rcm)(Es/3) = λ/e
=> λ = 2π(rcm)(Es/3)e
= 2π*r*(4.8 × 10^3/3)*(8.85*10^-12)
= 8.90*10^-8 r
[Plug in r to get the numerical value]
Figure (a) shows a narrow charged solid cylinder thatis coaxial with a larger charged cylindrical...
Figure (a) shows a narrow charged solid cylinder that is coaxial with a larger charged cylindrical shell. Both are nonconducting and thin and have uniform surface charge densities on their outer surfaces. Figure (b) gives the radial component E of the electric field versus radial distance r from the common axis. The vertical axis scale is set by Es = 4.5 x 103 N/C. What is the linear charge density of the shell?
Figure (a) shows a narrow charged solid cylinder that
is coaxial with a larger charged cylindrical shell. Both are
nonconducting and thin and have uniform surface charge densities on
their outer surfaces. Figure (b) gives the radial
component E of the electric field versus radial distance
r from the common axis. The vertical axis scale is set by
Es = 3.6 × 103 N/C. What is the
linear charge density of the shell?
E 0 14.4 -ES r(cm)
Figure (a) shows a narrow charged solid cylinder that is coaxial with a larger charged cylindrical shell. Both are nonconducting and thin and have uniform surface charge densities on their outer surfaces. Figure (b) gives the radial component E of the electric field versus radial distance r from the common axis. The vertical axis scale is set by Es = -4.8x 103 N/C. What is the linear charge density of the shell?
2. A modified coaxial cable consists of a solid cylinder (radius 'a') with a uniform current density and a concentric cylindrical conducting thin shell (radius 'b'). The outer and inner current have an equal magnitude, but are opposite in direction. Io (along outside) (along the axis) (off-axis view) In terms of radial distance 'r', and the relevant parameters in the diagram above, A) Derive an expression for the magnetic field inside the solid cylinder (r <a) B) Derive an expression...
Concentric Cylindrical Conducting Shells
1
An infiinitely long solid conducting cylindrical shell of radius
a = 4.8 cm and negligible thickness is positioned with its symmetry
axis along the z-axis as shown. The shell is charged, having a
linear charge density ?inner = -0.35 ?C/m. Concentric
with the shell is another cylindrical conducting shell of inner
radius b = 17.1 cm, and outer radius c = 21.1 cm. This conducting
shell has a linear charge density ? outer =
0.35?C/m....
Chapter 23, Problem 028 GO A charge of uniform linear density 3.00
nC/m is distributed along a long, thin, nonconducting rod. The rod
is coaxial with a long conducting cylindrical shell (inner radius =
6.00 cm, outer radius = 10.8 cm). The net charge on the shell is
zero. (a) What is the magnitude of the electric field at distance r
= 16.8 cm from the axis of the shell? What is the surface charge
density on the (b) inner and...
A long, conductive cylinder of radius R1 = 3.00 cm and uniform charge per unit length λ = 604 pC/m is coaxial with a long, cylindrical, non-conducting shell of inner and outer radii R2 = 10.5 cm and R3 = 12.0 cm, respectively. If the cylindrical shell carries a uniform charge density of p = 79.8 pC/m, find the magnitude of the electric field at the following radial distances from the central axis:
A long, conductive cylinder of radius R 2.70 cm and uniform charge per unit length 151 pC/m is coaxial with a long, cylindrical, nonconducting shell of inner and outer radii R2 9.45 cm and R3 10.8 cm, respectively. If the cylindrical shell carries a uniform charge density of p 79.8 pC/m3, find the magnitude of the electric field at the following radial distances from the central axis: Number 1.51 cm 0 N/C Number RR, R 6.08 cm 44.65 N/C Incorrect....
An infiinitely long solid conducting cylindrical shell of radius a = 4.8 cm and negligible thickness is positioned with its symmetry axis along the z-axis as shown. The shell is charged, having a linear charge density λinner = -0.51 μC/m. Concentric with the shell is another cylindrical conducting shell of inner radius b = 15 cm, and outer radius c = 17 cm. This conducting shell has a linear charge density λ outer = 0.51μC/m. 1.What is Ex(P), the x-component...
28 mm 49 Sim The cross section of a long coaxial cable is shown in the figure, with radil as given. The linear charge density on the inner conductor is 50 nC/m and the linear charge density on the outer conductor is -40 nC/m. The inner and outer cylindrical surfaces are respectively denoted by A, B, C and D, as shown. - 8,85 x 10-12</m?) The radial component of the electric field at a point that 32 mm from the...